Survival with Ambiguity

We analyze a market populated by expected utility maximizers and smooth ambiguity-averse consumers. We study conditions under which ambiguity-averse consumers survive and affect prices in the limit. If ambiguity vanishes with time or if the economy exhibits no aggregate risk, ambiguity-averse consumers survive, but have no long-run impact on prices. In both scenarios, ambiguity-averse consumers are fully insured against ambiguity in equilibrium and, thus, behave as expected utility maximizers with correct beliefs. If ambiguity-averse consumers are not fully insured against ambiguity, they behave as expected utility maximizers with effectively wrong beliefs and an effective discount factor which might be higher or lower than their actual discount factor. Using this insight, we demonstrate that consumers with constant absolute ambiguity aversion vanish in expectations, whenever the economy faces aggregate risk. In contrast, consumers with constant relative (and thus, decreasing absolute) ambiguity aversion survive in expectation and with positive probability and have a non-trivial impact on prices in the limit.